Selecting baseline two-level designs using optimality and aberration criteria when some two-factor interactions are important

The baseline parameterization is less commonly used in factorial designs than the orthogonal parameterization. However, the former is more natural than the latter when there exists a default or preferred setting for each factor in an experiment. The current method selects optimal baseline designs for estimating a main effect model. In this project, we consider the selection of optimal baseline designs when estimates of both main effects and some two-factor interactions are wanted. Any other potentially active effect causes bias in estimation of the important effects. To minimize the contamination of these potentially active effects, we propose a new minimum aberration criterion. Moreover, an optimality criterion is used to minimize the variances of the estimates. Finally, we develop a search algorithm for selecting optimal baseline designs based on these criteria and present some optimal designs of 16 and 20 runs for models with up to three important two-factor interactions.